2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228645We consider light scattering from ultracold atoms trapped in an optical lattice into a cavity. The measurement of photons leaking out the cavity provides a quantum nondemolition (QND) access to various atomic variables. Depending on the chosen geometry the time resolved light detection projects the atomic quantum state to various atom-number squeezed and Schroedinger cat states. Modifications of the atomic and light properties at a single quantum trajectory are demonstrated. The quantum structure of final states can be revealed by further observations of the same sample.4 pages, 3 figuresQuantum PhysicsOther Condensed MatterAtomic PhysicsOpticstext